## Related questions with answers

In a science class lab, a mass is suspended from a spring above a tabletop. The mass is pulled down and released. By examining frames from a video as the mass bobs up and down, the class obtains the model h(t)=5 $\sin 4(t-0.39)+10$ for the height h of the mass above the tabletop at time $t$ in seconds. Cassandra notices that after several seconds the mass is not bobbing up and down as far, but it still seems to take about the same time for a cycle. Plot $y=e^{-0.05 x}[5 \sin 4(x-0.39)]+10$ on a graphing calculator with the original model for $0 \leq x \leq 10$. State how this model differs from the original model, and how it might account for Cassandra's observation.

Solution

VerifiedThe task is to graph the given functions and then to compare them. The functions are:

$\begin{aligned}h(t) &= 5\sin4(t-0.39)+10\\ \\ y&=e^{-0.05x}[5\sin 4(t-0.39)] + 10, \text{ for } 0 \le x\le 10. \end{aligned}$

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